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# How many different anagrams can you make for the word MATHEM

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How many different anagrams can you make for the word MATHEM [#permalink]

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22 Apr 2014, 06:07
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How many different anagrams can you make for the word MATHEMATICS?

I donot have any options...but the correct answer here is 8!/2!

I don't understand how?
Should it not be 11!/(2!*2!*2!)
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Math Expert
Joined: 02 Sep 2009
Posts: 43810
Re: How many different anagrams can you make for the word MATHEM [#permalink]

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22 Apr 2014, 06:22
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JusTLucK04 wrote:
How many different anagrams can you make for the word MATHEMATICS?

I donot have any options...but the correct answer here is 8!/2!

I don't understand how?
Should it not be 11!/(2!*2!*2!)

Your solution is correct. The correct answer is indeed 11!/(2!*2!*2!): the number of arrangement of 11 letters out of which 2 A's, 2 M's and 2 T's are the same.

Similar but much harder question to practice: how-many-words-can-be-formed-by-taking-4-letters-at-a-time-92675.html

THEORY:

Permutations of $$n$$ things of which $$P_1$$ are alike of one kind, $$P_2$$ are alike of second kind, $$P_3$$ are alike of third kind ... $$P_r$$ are alike of $$r_{th}$$ kind such that: $$P_1+P_2+P_3+..+P_r=n$$ is:

$$\frac{n!}{P_1!*P_2!*P_3!*...*P_r!}$$.

For example number of permutation of the letters of the word "gmatclub" is 8! as there are 8 DISTINCT letters in this word.

Number of permutation of the letters of the word "google" is $$\frac{6!}{2!2!}$$, as there are 6 letters out of which "g" and "o" are represented twice.

Number of permutation of 9 balls out of which 4 are red, 3 green and 2 blue, would be $$\frac{9!}{4!3!2!}$$.

Hope this helps.
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Re: How many different anagrams can you make for the word MATHEM [#permalink]

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22 Apr 2014, 06:28
Thanks Bunuel..I have been through this post and already using the Math Book and Veritas as my primary source of practice..
This was just to confirm my solution..
Thank you again for the quick replies every time I am stuck some where..
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Re: How many different anagrams can you make for the word MATHEM [#permalink]

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02 Oct 2017, 05:57
JusTLucK04 wrote:
How many different anagrams can you make for the word MATHEMATICS?

I donot have any options...but the correct answer here is 8!/2!

I don't understand how?
Should it not be 11!/(2!*2!*2!)

The correct solution is as provided by you and it should be 11!/(2!*2!*2!)

MATHEMATICS = MM AA TT HEICS
So, total 11 letters to be arranged in 11! ways and divided by 2! each for the duplicates created by MM, AA, TT which can be arranged among themselves in 2! ways.
= 11!/(2!*2!*2!)
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Re: How many different anagrams can you make for the word MATHEM [#permalink]

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10 Jan 2018, 12:50
Hi there!

The word OTTO has 4 distinguishable anagrams:
OTTO
OTOT
TOTO
TOOT
But according to the formula it should be 4!/(2!*2!)=6. What am I missing here?
Math Expert
Joined: 02 Sep 2009
Posts: 43810
Re: How many different anagrams can you make for the word MATHEM [#permalink]

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10 Jan 2018, 19:33
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Spacegryphon wrote:
Hi there!

The word OTTO has 4 distinguishable anagrams:
OTTO
OTOT
TOTO
TOOT
But according to the formula it should be 4!/(2!*2!)=6. What am I missing here?

OOTT
OTOT
TOOT
TOTO
TTOO
OTTO

6 cases.
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Re: How many different anagrams can you make for the word MATHEM [#permalink]

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11 Jan 2018, 10:44
How could I overlook those...
Re: How many different anagrams can you make for the word MATHEM   [#permalink] 11 Jan 2018, 10:44
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